David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Mind 109 (435):455-480 (2000)
According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of sentences in the nominalist language such theories entail. However, I argue that what such theories show is that mathematics can enable us to express possibilities about the concrete world that may not be expressible in nominalistically acceptable language. While I grant that this may make quantification over abstracta indispensable, I deny that such indispensability is a reason for accepting them into our ontology. I urge that the nominalist should be allowed to quantify over abstracta whilst denying their existence and I explain how this apparently contradictory practice (a practice I call 'weaseling') is in fact coherent, unproblematic and rational. Finally, I examine the view that platonistic theories are simpler or more attractive than their nominalistic reformulations, and thus that abstract ought to be accepted into our ontology for the same sorts of reasons as other theoretical objects. I argue that, at least in the case of numbers, functions and sets, such arguments misunderstand the kind of simplicity and attractiveness we seek.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Robert Batterman (2010). On the Explanatory Role of Mathematics in Empirical Science. British Journal for the Philosophy of Science 61 (1):1-25.
Juha Saatsi (2011). The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science. British Journal for the Philosophy of Science 62 (1):143-154.
Mark Colyvan (2010). There is No Easy Road to Nominalism. Mind 119 (474):285 - 306.
Theodore Sider (2006). Bare Particulars. Philosophical Perspectives 20 (1):387–397.
Jonathan Tallant (2009). Ontological Cheats Might Just Prosper. Analysis 69 (3):422-430.
Similar books and articles
Otávio Bueno (2003). Quine's Double Standard: Undermining the Indispensability Argument Via the Indeterminacy of Reference. Principia 7 (1-2):17-39.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Charles Chihara (2010). New Directions for Nominalist Philosophers of Mathematics. Synthese 176 (2):153 - 175.
A. Baker (2003). Does the Existence of Mathematical Objects Make a Difference? Australasian Journal of Philosophy 81 (2):246 – 264.
Patrick S. Dieveney (2007). Dispensability in the Indispensability Argument. Synthese 157 (1):105 - 128.
Chris Daly & Simon Langford (2011). Two Anti-Platonist Strategies. Mind 119 (476):1107-1116.
Added to index2009-01-28
Total downloads74 ( #45,843 of 1,726,249 )
Recent downloads (6 months)8 ( #84,767 of 1,726,249 )
How can I increase my downloads?